Fast and generalizable micromagnetic simulation with deep neural nets

Abstract

Important progress has been made in micromagnetics, driven by its wide-ranging applications in magnetic storage design. Numerical simulation, a cornerstone of micromagnetics research, relies on first-principles rules to compute the dynamic evolution of micromagnetic systems using the renowned Landau–Lifshitz–Gilbert equation, named after Landau, Lifshitz and Gilbert. However, these simulations are often hindered by their slow speeds. Although fast Fourier transformation calculations reduce the computational complexity to O(Nlog(N)), it remains impractical for large-scale simulations. Here we introduce NeuralMAG, a deep learning approach to micromagnetic simulation. Our approach follows the Landau–Lifshitz–Gilbert iterative framework but accelerates computation of demagnetizing fields by employing a U-shaped neural network. This neural network architecture comprises an encoder that extracts aggregated spins at various scales and learns the local interaction at each scale, followed by a decoder that accumulates the local interactions at different scales to approximate the global convolution. This divide-and-accumulate scheme achieves a time complexity of O(N), notably enhancing the speed and feasibility of large-scale simulations. Unlike existing neural methods, NeuralMAG concentrates on the core computation—rather than an end-to-end approximation for a specific task—making it inherently generalizable. To validate the new approach, we trained a single model and evaluated it on two micromagnetics tasks with various sample sizes, shapes and material settings.